BROKEN ERGODICITY AND GLASSY BEHAVIOR IN A DETERMINISTIC CHAOTIC MAP

A network of N elements is studied in terms of a deterministic globall y coupled map which can be chaotic. There exists a range of values for the parameters of the mag where the number of different macroscopic c onfigurations N(N) is very large, N(N) similar to exp root c(a)N, and there is violation of self-averaging. The time averages of functions, which depend on a single element, computed over a time T, have probabi lity distributions that for any N do not collapse to a delta function, for increasing T. This happens for both chaotic and regular motion, i .e., positive or negative Lyapunov exponent.